A physiologically based, multi-scale model of skeletal muscle structure and function

Models of skeletal muscle can be classified as phenomenological or biophysical. Phenomenological models predict the muscle's response to a specified input based on experimental measurements. Prominent phenomenological models are the Hill-type muscle models, which have been incorporated into rigid-body modelling frameworks, and three-dimensional continuum-mechanical models. Biophysically based models attempt to predict the muscle's response as emerging from the underlying physiology of the system. In this contribution, the conventional biophysically based modelling methodology is extended to include several structural and functional characteristics of skeletal muscle. The result is a physiologically based, multi-scale skeletal muscle finite element model that is capable of representing detailed, geometrical descriptions of skeletal muscle fibres and their grouping. Together with a well-established model of motor unit recruitment, the electro-physiological behaviour of single muscle fibres within motor units is computed and linked to a continuum-mechanical constitutive law. The bridging between the cellular level and the organ level has been achieved via a multi-scale constitutive law and homogenisation. The effect of homogenisation has been investigated by varying the number of embedded skeletal muscle fibres and/or motor units and computing the resulting exerted muscle forces while applying the same excitatory input. All simulations were conducted using an anatomically realistic finite element model of the Tibialis Anterior muscle. Given the fact that the underlying electro-physiological cellular muscle model is capable of modelling metabolic fatigue effects such as potassium accumulation in the T-tubular space and inorganic phosphate build-up, the proposed framework provides a novel simulation-based way to investigate muscle behaviour ranging from motor unit recruitment to force generation and fatigue.